1. Field of the Invention
This invention relates to apparatus for monitoring and/or protecting alternating current (AC) electric power systems and, in particular, to apparatus, such as electronic protective relays, which provide on-line measurement of frequency of waveforms in such AC electric power systems. The invention also relates to a method for determining frequency of an AC signal of an electric power system.
2. Background Information
Frequency estimation is a very important function in power system protection. Frequency is not only an indication of power quality, but is also employed as a criterion for taking certain system control actions, such as load shedding. In addition, many protection functions and settings are based on the nominal frequency. In reality, power system frequency changes from time to time around the nominal value. Even through the variation from the nominal value is often very small, it may still make a significant difference in frequency-related applications. For instance, the voltage and current phasors, which are essential to implement many metering and relay functions, are obtained based on the nominal power frequency through use of Discrete Fourier Transform (DFT). A deviation from the nominal frequency will result in errors in both magnitude and phase of the phasor and, in turn, these errors will migrate into metering and relaying functions. If accurate frequency estimation could be obtained, then these errors would be minimized or eliminated.
The most popular methods for frequency measurement available today are the zero-crossing and DFT based techniques. As is well known, the accuracy of the zero-crossing method is influenced by harmonics but can be improved by using the least square technique or other noise-suppressing techniques. On the other hand, in the DFT based method, whether based on the magnitude or phase angle of a phasor, if all three-phase voltages are not available, then the estimated frequency will be oscillatory when the system frequency deviates from the nominal frequency. This oscillatory frequency is double the system frequency. The envelope of the estimated frequency increases with increasing deviation from the nominal frequency. Usually, the oscillatory frequency is smoothed through use of an average filter. However, with such a filter, the estimated frequency becomes stationary only at certain system frequencies while remaining oscillatory for other deviant system frequencies. It can be shown that with an average filter, the envelope of the estimated frequency will be a standing wave of increasing amplitude as the deviation from the nominal frequency increases. The standing points are dependent on the length of the average filter used. For instance, a two-cycle filter will result in three standing points at which the system frequencies are multiples of one-fourth the nominal frequency. This means that the estimation accuracy is system frequency dependent. An accurate frequency is only obtained at the standing points. An accurate estimation over a wide range of frequencies may be achieved by using adaptive approaches. These include the adaptive sampling period, the adaptive length of the data window, and adaptive filtering. Unfortunately, all of the adaptive approaches involve a considerable amount of computation in order to achieve better results.
A typical protective relay meters frequency and provides over/under frequency protection. Frequency is determined, for example, by employing a suitable measuring period (e.g., one or more line cycles) and by counting processor clocks between voltage zero crossings. However, electrical noise causes jitter on the zero crossings, thereby creating errors. Furthermore, averaging slows down the response time, although it improves accuracy.
There is a need therefore, for an improved apparatus for determining the frequency in an alternating current (AC) electric power system.
There is a further need for such an apparatus, which provides such an estimation of frequency with a consistent and predictable accuracy.
There is also a need for such an apparatus, which does not require excessive calculation, and can, therefore, provide an accurate estimation of frequency on-line with a reasonable computational burden and cost.
These needs and others are satisfied by the present invention, which is directed to an apparatus for providing an accurate on-line indication of frequency in an alternating current (AC) electric power system.
As one aspect of the invention, an apparatus determines frequency of an AC signal of an electric power system. The apparatus comprises means for measuring the period of the AC signal between one zero crossing and a subsequent zero crossing of the AC signal to provide a measured period value; and a processor comprising: a memory collecting at least five consecutive values of the measured period values, and a routine choosing a median value from the measured period values and determining the frequency based upon the median value.
The routine of the processor may further employ the median value to determine a new line cycle period if: (i) an absolute value of a difference between a last value of the measured period values and a previously determined line cycle period is less than a predetermined value; or (ii) the last value of the measured period values is greater than or equal to or less than or equal to all of the measured period values; and, otherwise, adjusts the previously determined line cycle period to determine the new line cycle period. The processor routine may predetermine the predetermined value from the previously determined line cycle period divided by a first constant minus a second constant.
As another aspect of the invention, a method for determining frequency of an AC signal of an electric power system comprises measuring the period of the AC signal between one of the zero crossings and a subsequent one of the zero crossings to provide a measured period value; collecting at least five consecutive values of the measured period values; choosing a median value from the consecutive values of the measured period values; and determining the frequency based upon the median value.
For example, statistical techniques are employed to measure the period of the line cycle by maintaining the last five line cycle period measurements, period(1), period(2), period(3), period(4), period(5), in a five-element array, period(n). In turn, the median value of the array is employed as the new line cycle period, P0, in place of the old line cycle period, Pxe2x88x921, if: (i) |last line cycle period measurement, period(1)xe2x88x92Pxe2x88x921| is less than Pxe2x88x921/512xe2x88x9213; or (ii) the period(1) is not within the limits (i.e., period(1) is greater than or equal to the maximum value, period(n)MAX, of the array, or is less than or equal to the minimum value, period(n)MIN, of the array) of the last five line cycle period measurements in the array.
As another aspect of the invention, a method for determining frequency of an AC signal of an electric power system comprises measuring the period of the AC signal between one of the zero crossings and a subsequent one of the zero crossings to provide a measured period value; collecting at least five of the measured period values; determining at least two highest values of the measured period values; determining at least two lowest values of the measured period values; and determining the frequency based upon the measured period values excluding the at least two highest values and the at least two lowest values.
The method may employ an odd count or an even count of the measured period values. For example, the method may employ five as the odd count of the measured period values, may determine a median value of the measured period values, and may determine the frequency based upon the median value.
The method may determine an average value of the measured period values excluding the two highest values and the two lowest values, and may determine the frequency based upon the average value.
The method may employ at least six as the even count of the measured period values, may determine two values closest to a median of the measured period values, may determine an average value of such two values, and may determine the frequency based upon such average value.